SOLUTION: The answer that I have come up with is: (e -1).2: The problem is what are the exact evaluation of, (integral sign), 2xe^(x^2) dx over the intervals (0, 1). I feel this is

Question 127249: The answer that I have come up with is: (e -1).2:
The problem is what are the exact evaluation of, (integral sign), 2xe^(x^2) dx over the intervals (0, 1). I feel this is not correct, can you verify that for me please?
Also please, I have determined that In x is not the correct completion of the formula, (integral sign), (1/x). Is that correct, or should I do more research on this subject?
Thank you all, for your God given talent that helps us less fortunate.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given integral

Let . So this means that . So the gets replaced with and the (you have to group these together) gets replaced with

Also, since the first endpoint is 0, this means that . But we want this in terms of u. So just plug in into to get . Do the same thing with the other endpoint to get

So we now have:

So we now have:
Take the integral of to get . Remember

Now let's evaluate the endpoints

Plug in the endpoints and subtract

Combine like terms and simplify

So

--------------------------------------

Are you trying to evaluate ?

The integral of is . In other words,
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SOLUTION: The answer that I have come up with is: (e -1).2: The problem is what are the exact evaluation of, (integral sign), &#61682;2xe^(x^2) dx over the intervals (0, 1). I feel this is

SOLUTION: The answer that I have come up with is: (e -1).2: The problem is what are the exact evaluation of, (integral sign), 2xe^(x^2) dx over the intervals (0, 1). I feel this is